A particle is executing SHM with time period π $$sec$$ along a straight line. At $$t=0$$, it has started its motion from one of its extreme position. Then the minimum time after which its kinetic energy will be equal to its potential energy is

Question

A particle is executing SHM with time period π $$sec$$ along a straight line. At $$t=0$$, it has started its motion from one of its extreme position. Then the minimum time after which its kinetic energy will be equal to its potential energy is

Infinity Learn · Accepted Answer

Equation of SHM is  $$x=Acos$$ωt At time t , potential energy,  $$U=12m$$ω$$2x2=12m$$ω$$2A2cos2$$ωtAnd kinetic energy, $$K=12m$$ω$$2(A2$$−$$x2)=12m$$ω$$2A2sin2$$ωtWhen $$K=U$$, $$12m$$ω$$2A2sin2$$ω$$t=12m$$ω$$2A2cos2$$ωt ⇒$$tan$$ω$$t=$$±$$1$$⇒ω$$t=$$π$$4$$,$$3$$$$π$$$$4$$,$$5$$$$π$$$$4$$,$$7$$$$π$$$$4$$,........etc∴$$tmin=$$π$$4$$ω$$=$$π$$4$$×$$2$$ππ$$=$$π$$8sec$$

Simple hormonic motion

Remember concepts with our Masterclasses.

A particle is executing SHM with time period π sec along a straight line. At t=0, it has started its motion from one of its extreme position. Then the minimum time after which its kinetic energy will be equal to its potential energy is

Ready to Test Your Skills?

free study material

Simple hormonic motion

Remember concepts with our Masterclasses.

A particle is executing SHM with time period π sec along a straight line. At t=0, it has started its motion from one of its extreme position. Then the minimum time after which its kinetic energy will be equal to its potential energy is

Equation of SHM is x=Acosωt At time t , potential energy, U=12mω2x2=12mω2A2cos2ωtAnd kinetic energy, K=12mω2(A2−x2)=12mω2A2sin2ωtWhen K=U, 12mω2A2sin2ωt=12mω2A2cos2ωt ⇒tanωt=±1⇒ωt=π4,3π4,5π4,7π4,........etc∴tmin=π4ω=π4×2ππ=π8sec

Ready to Test Your Skills?

free study material